For the Mornay sauce: Add the butter to a medium pot set over medium heat. Add the flour and cook, whisking, until blonde in color, 2 to 3 minutes. Slowly whisk in 1 cup of the milk until combined. Add the Gruyere, mustard and nutmeg and simmer, whisking occasionally, until thick, about 10 minutes. Season with salt and white pepper. Keep warm over low heat, whisking occasionally and adding up to 1/2 cup additional milk to thin if needed, until ready to plate.
For the corned beef hash: Heat a medium pan over medium heat. Add the oil and shallots and saute until translucent and slightly golden, about 10 minutes. Add the corned beef and saute until crispy and browned, 5 to 7 minutes more.
For serving: Butter the English muffin halves and drizzle with a bit of honey. Sprinkle the tomato slices with salt, then place a couple slices on top of each muffin half, followed by some hash. Top with a sunny-side up egg and ladle Mornay sauce on top. Garnish with minced chives.